1. Field of the Invention
This invention relates to a computer method and system for providing optimization for manufacturing processes.
2. Introduction to the Invention
The invention is introduced by first setting forth the following known construct.
Given a functional form y=f(x,b) where x is a set of independent controllable variables x={(x1, . . . xn}, b is a set of manufacturing variables (functional parameters) b={b1, . . . bm}, and y is a dependent uncontrollable variable, it is desired to optimize (e.g., maximize, minimize) f(x,b), i.e. Derive a set b*={b1*, . . . , bm*} which optimizes f(x,b) for an historical dataset comprising observations of independent variables x and their corresponding dependent variable y, subject to constraints on the dependent uncontrollable variable y, say g(y) greater than 0.
Now, if the constraints were on the manufacturing parameters b, this would be normally solved as a mathematical programming problem (linear, quadratic or nonlinear programming). Here, in contrast, the constraints are on the dependent uncontrollable variable y. Accordingly, in order to still utilize the powerful mathematical programming techniques, it is necessary to convert the constraints on y to constraints on b using the functional estimate of y and its manufacturing parameters b (e.g., g(y)=gf(x,b) greater than 0).
In turn, operating on historical data (sets of x and associated y) thus yields complete functional description, fully satisfying the given constraints.
The present invention is cognizant of the aforementioned functional construct. Moreover, the present invention builds upon this known functional construct, but references this known construct to impose upon it novel problems, constraints, and desiderataxe2x80x94of the following illustrative type.
Accordingly, to compute y at a new set of controllable variables, say xxe2x80x2, one cannot simply plug xxe2x80x2 into the currently optimized f(xxe2x80x2,b*), which is based on the historical data, because there is no guarantee that the resulting yxe2x80x2 will satisfy the constraints on the dependent variable, g(yxe2x80x2) greater than 0.
To insure satisfaction of the constraint at the new point xxe2x80x2 we propose to add f(xxe2x80x2,b) to the set of constraints (e.g., add gf(xxe2x80x2,b) greater than 0 to the constraints), and re-run the mathematical program with the new set of constraints. Note that this may affect the resulting function f(x,b) by yielding a new set b**, even though no measurements at the new point xxe2x80x2 were performed or observed.
If it is desired to compute values of the dependent variable at several new points, then three cases may be considered:
1) if the new points are ordered (e.g., forecasting), the preferred method is to perform sequential adding of the appropriate constraints;
2) if the new points are not ordered, one can derive y for each new point based only on historical data and its own contribution to the set of constraints;
3) alternatively, one can simultaneously derive y for all new points by adding all associated new constraints to the historical set.
We now restate these invention discoveries, by disclosing a first aspect of the present invention comprising a novel computer method for providing optimization for manufacturing processes for situations wherein there is defined a functional form y=f(x,b), where x comprises a set of independent controllable variables x={x1, . . . xn}, b comprises a set of functional parameters b={b1, . . . bm}, and y comprises a dependent uncontrollable manufacturing variable, f(x,b), subject to constraints on the dependent uncontrollable manufacturing variable y, the method comprising the steps of
(i) converting the constraints on y to constraints on b by using a functional estimate of y and its manufacturing variables (parameters) b;
(ii) optimizing the function f(x,b) subject to the converted constraints on its independent manufacturing variables (parameters) b; and
(iii) generating from step (ii) a set of optimized values of b which can optimize the dependent manufacturing variable y.
Preferably, the method comprises a step (iv) of computing the dependent manufacturing variable y at a new set of the independent variables x, said x not being part of an historical set of x variables inherited from step (ii). In particular, this step preferably further comprises guaranteeing that the computed y satisfies the constraints on the dependent manufacturing variable y at the new set of independent variables x.
Preferably, the method can alternatively comprise a step (iv) of computing values of the dependent manufacturing variable at several new points of the independent variable x. In particular, this step preferably further comprises steps of determining that the new points are ordered, and, sequentially adding the appropriate constraints.
Preferably, moreover, the method can alternatively comprise steps of determining that the new points are not ordered, and, deriving why at each new point based only on historical data and y""s own contribution to the set of constraints.
The method as summarized also includes an advantageous capability comprising the steps of computing values of the dependent manufacturing variable at several new points of the independent variables x, and, simultaneously deriving y for all new points by a step of adding all associated new constraints to the historical set.
In a second aspect of the present invention, we disclose a program storage device, readable by machine to perform method steps for providing optimization for manufacturing processes for situations wherein there is defined a functional form y=f(x,b), where x comprises a set of independent controllable variables x={x1, . . . xn}, b comprises a set of functional parameters b={b1, . . . bm}, and y comprises a dependent uncontrollable manufacturing variable f(x,b) subject to constraints on the dependent uncontrollable manufacturing variable y, the method comprising the steps of:
(i) converting the constraints on y to constraints on b by using a functional estimate of y and its manufacturing variables (parameters) b;
(ii) optimizing the function f(x,b) subject to the converted constraints on its manufacturing variables (parameters) b; and
(iii) generating from step (ii) a set of optimized values of b which optimizes the dependent manufacturing variable y.
In a third aspect of the present invention, we disclose a computer for providing optimization for manufacturing processes, the computer comprising:
(i) means for inputting data defining a functional form y=fx,b), where x comprises a set of independent controllable variables x={x1, . . . xn}, b comprises a set of functional parameters b={b1, . . . bm}, and y comprises a dependent uncontrollable manufacturing variable, f(x,b) subject to constraints on the dependent uncontrollable manufacturing variable y;
(ii) means for converting the constraints on y to constraints on x by using a functional estimate of y and its manufacturing variables (parameters) b;
(iii) means for optimizing the function f(x) subject to the converted constraints on its manufacturing variables (parameters) b;
(iv) means for generating from element (iii) a set of optimized values of b which optimizes the dependent manufacturing variable y; and
(v) means for displaying the set of optimized values of b and the resulting manufacturing variable y.